An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is 3.6 × 10 –5 /ºC)
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Initial diameter of tyre = (1000 – 6) mm = 994 mm , so initial radius of tyre 
and change in diameter Δ Δ D = 6 mm so 
After increasing temperature by Δ Δ θ θ tyre will fit onto wheel
Increment in the length (circumference) of the iron tyre
Δ Δ L = L × × α α × × Δ Δ θ θ 
[As 
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